Friday, June 15, 2012

Montage # 59 - The Fibonacci Sequence / La suite de Fibonacci

As of July 20, 2012, this montage will no longer be available on Pod-O-Matic. It can be heard or downloaded from the Internet Archive at the following address / A compter du 20 juillet 2012, ce montage ne sera plus disponible en baladodiffusion Pod-O-Matic. Il peut être téléchargé ou entendu au site Internet Archive à l'adresse suivante:

In the book Liber Abaci (Translation: The Book of Calculation, published in 1202), the author considers the growth of an idealized (biologically unrealistic) rabbit population:

A newly born pair of rabbits, one male, one female, are put in a field; rabbits are able to mate at the age of one month so that at the end of its second month a female can produce another pair of rabbits; rabbits never die and a mating pair always produces one new pair (one male, one female) every month from the second month on.

How many pairs will there be in one year?

The author of the book, Leonardo of Pisa, known as Fibonacci, thus presents the first documented example of what has come to be known as the Fibonacci sequence, that is the number of pairs of rabbits after each month:

0, 1, 1, 2, 3, 5, 8, 13, .., each number being derived as the sum of the two preceeding entries in the sequence, or

Fibonacci may have been the first western mathematician to have brought up the sequence, but the development of the Fibonacci sequence is attributed in part to Eastern mathematicians: Pingala (200 BC), Virahanka (c. 700 AD), Gopāla (c. 1135), and Hemachandra (c. 1150).

Some of you may remember the sequence being part of the at times twisted plot in the Dan Brown novel (and the Ron Howard motion picture) The DaVinci Code. Or this parody...

To illuistrate the sequence in the context of our “Music by the Numbers” montages, I will rely on a major work - the op. 1 caprices for solo violin by Paganini in the reference mono recording by Ruggiero Ricci. The entire recording is availabvle at:

The number “0” is represented by a movement from Bruckner’s Symphony no. 0 - Die Nullte (translated to The Zeroth, not to be confused with his symphony “00”, or his Studiensymphonie). The remainder of the sequence is illustrated by two feature works.

Czech composer Antonin Dvořák – a favourite of this blog – was a prolific chamber music composer. Over a period of almost 30 years, Dvořák's output of chamber music consists of more than 40 works for ensembles with strings, including at least 14 string quartets, as well as a number of works for quartet that don’t follow the usual pattern (thinking here of theCypřiše (or Cypresses).

Though his most famous quartet may very well be his American (his op. 96), this charming op. 34 pre-dates his American stay by 15 years. Dvořák was a champion of folk music, and this quartet has all the charm and earmarks of what made him successful with audiences.

Edvard Grieg composed nearly two hours of music for Ibsen’s play Peer Gynt (Grieg’s op. 23) , most of which is worth listening to in context of the play. However, rightly or wrongly, the Peer Gynt music is most often heard in the form of the two concert suites Grieg assembled (his opp. 46 and 55). Where the first suite contains some of the most famous and enduring passages of the incidental music (the Morning Mood and the Hall of the Mountain King), the second suite has more the feel of being a set of Grieg’s favourites – and the song that Solveig sings in Act 4 of the play is hauntingly beautiful. The suite provides only the instrumental backdrop – the French commentary embeds the song with soprano Lucia Popp.